Physics of Radiography

Transcription

1 EL-GY 6813 / BE-GY 6203 / G Medical Imaging Physics of Radiography Jonathan Mamou and Yao Wang Polytechnic School of Engineering New York University, Brooklyn, NY Based on Prince and Links, Medical Imaging Signals and Systems and Lecture Notes by Prince. Figures are from the book.

2 Lecture Outline Atomic structure and ionization Particulate Radiation Focusing on energetic electron interaction EM Radiation Photoelectric Compton scattering -> Likelihood of each phenomenon EM radiation measurement Attenuation of radiation Radiation Dosimetry Exposure, dose Radiation Physics Yao Wang, NYU 2

3 An atom={a nucleus, electrons} Atomic Structure Nucleus composed of nucleons = {protons; neutrons} mass number A = # nucleons atomic number Z = # protons = # electrons Define an element with a particular symbol: H, C, etc. An element is denoted by its A and Z 12 Ex: or C C Radiation Physics Yao Wang, NYU 3

4 Stable vs. Unstable States Stable nuclides: # neutrons ~= # protons (A ~= 2Z) Unstable nuclides (radionuclides, radioactive atoms) Likely to undergo radioactive decay, which gives off energy and results in a more stable nucleus Radiation Physics Yao Wang, NYU 4

5 Orbits of Electrons Ground state: electrons are in the lowest orbital shells and within the lowest energy quantum states within each shell Radiation Physics Yao Wang, NYU 5

6 Electron Binding Energy A free electron has higher energy than when it is bounded to an nucleus in an atom Binding energy = energy required to free electrons from their atomic orbits Depends on the element to which the electron is bound and the shell within which it resides in ground state Sufficient to consider average binding energy of a given atom One electron volt (ev) = kinetic energy gained by an electron when accelerated across one volt potential 1 ev = 1.6 x Joule Binding energies of typical elements: hydrogen = 13.6 ev Air: 29 ev Lead: 1 KeV Tungsten: 4 KeV (considered a heavy element) Electronvolt (ev) is a unit of energy equal ~ J. It is the amount of energy gained (or lost) by the charge of a single electron moving across a 1-V electric potential difference -> 1 volt (= 1 J/C) multiplied by the elementary charge (e, or ~ C). 1 ev = J. Radiation Physics Yao Wang, NYU 6

7 Ionization and Excitation Ionization is knocking an electron out of an atom Creates a free electron + ion (an atom with +1 charge) Occurs when radiated with energy above the electron binding energy Excitation is knocking an electron to a higher orbit When the radiation energy is lower than the binding energy After either ionization or excitation, an atom has higher energy Radiation Physics Yao Wang, NYU 7

8 Characteristic Radiation What happens to ionized or excited atom? Return to ground state by rearrangement of electrons Causes atom to give off energy Energy given off as characteristic radiation infrared light x-ray Radiation Physics Yao Wang, NYU 8

9 Example Consider an electron accelerated through an X-ray tube where the anode is made of tungsten. If the anode is held at 120 KV, what is the maximum number of tungsten atoms that can be ionized? Solution: The electron will have 120 KeV kinetic energy when reaching the anode, by definition of ev The average binding energy of tungsten = 4 KeV # ionized atoms = 120/4=30 Radiation Physics Yao Wang, NYU 9

10 Ionizing Radiation Radiation Physics Yao Wang, NYU 10

11 Two Types of Ionizing Radiation Particulate Electro-magnetic (EM) Radiation Physics Yao Wang, NYU 11

12 Particulate Radiation Radiation by any particle (proton, neutron or electron) if it possesses enough kinetic energy to ionize an atom Kinetic Energy = the energy gained due to motion m0 Mass of a moving particle : m = 2 1 v 2 c 2 Energy vs. mass : E = mc Kinetic Energy : KE = E E0 = ( m m When v << c, 1+ v 2, KE 2 1 v 2 c 2 c 0 2 ) c 1 = 2 m v 0 2 Radiation Physics Yao Wang, NYU 12

13 Particulate Radiation by Energetic Electrons We are only concerned with an electron accelerated in a X-ray tube here An electron accelerated across a tube with 100 KV potential possesses 100 KeV kinetic energy Radiation Physics Yao Wang, NYU 13

14 Energetic Electron Interactions Two primary interactions Collisional transfer Most common Produces heat Radiative transfer Produces x-ray Characteristic radiation Collide with K-shell Bremsstrahlung radiation ( Braking or deceleration radiation ) Collide with nucleus More common than characteristic radiation Radiation Physics Yao Wang, NYU 14

15 Collisional Transfer The energetic electron collides with an atom in the target Typically, a small fraction of the kinetic energy of the electron is transferred to another electron in the atom As the affected atom returns to its original state, infrared radiation (heat) is generated Occasionally, a large fraction of the incident energy is transferred to another electron, the newly freed electron may form a delta ray The incident electron s path may be redirected, and many other subsequent interactions may occur, until the kinetic energy of the incident electron is exhausted Radiation Physics Yao Wang, NYU 15

16 Characteristic X-Ray The incident electron collides with a K-shell electron, exciting or ionizing the atom, leaving a hole in that shell. As the atom returns to its ground state, the k-shell hole is filled by a higher shell electron The loss of energy creates an EM photon, known as Characteristic x-ray The energy of the x-ray photon = difference between the energy of the two shells (element dependent) Radiation Physics Yao Wang, NYU 16

17 Characteristic radiation Caused by removal of inner shell electrons and subsequent filling of hole with electrons from higher shell. The shell-energy difference determines the energy of characteristic rays Lines are named after the lower shell involved in the process; the upper shell involved is denoted by Greek letters: - M - L K hν N M L K Continuum α β L-lines α β γ E [kev] K γ K β K α K-lines [From Graber, Lecture Note for BMI1-FS05] Radiation Physics Yao Wang, NYU 17

18 Different types of characteristics rays From Radiation Physics Yao Wang, NYU 18

19 Bremsstrahlung Ray As the incident electron approaches the nucleus of an atom, the positive charge of the nucleus causes the incident electron to bend around the nucleus and decelerates The loss of energy leads to the Bremsstrahlung x-ray (energy vary over a continuous range, depending on the speed loss) Occasionally when the incident electron collides with the nucleus, the electron is annihilated, emitting a photon with an energy equal to the kinetic energy of the incident electron (highest possible energy) Primary source of x-rays from an x-ray tube Radiation Physics Yao Wang, NYU 19

20 Spectrum of X-Ray Different curves are generated when different voltage potentials applied in a x-ray tube Generated when K-shell electrons are replaced by different outer shells When the incident electron collides with a nucleus Radiation Physics Yao Wang, NYU 20

21 EM Radiation EM radiation comprises an electric wave and a magnetic wave traveling at right angles to each other Typical EM waves: Non ionizing: radio, microwaves, infrared, visible light, ultraviolet Ionizing: X-rays, gamma rays Energy of a photon of an EM wave with frequency v: Radiation Physics Yao Wang, NYU 21

22 EM Waves for Medical Imaging X-rays and Gamma rays: Have energy in the KeVs to MeVs -> Ionizing Radiation used in X-ray/CT and nuclear medicine respectively X-rays are created by interaction of energetic electrons with atoms Gamma rays are created in the nuclei of atoms due to radioactive decay or characteristic radiation, typically have higher energy than X-rays Radio waves Used to stimulate nuclei in MRI to generate EM radiation Visible light Used in radiography to improve the efficiency of photographic film to detect X-rays See Table 4.2 for more details Radiation Physics Yao Wang, NYU 22

23 EM Radiation Interactions Two main interactions Photoelectric effect The incoming photon is completely absorbed and ejecting K-shell or L-shell electrons, producing characteristic x-ray Compton scattering The incoming photon changes its direction Radiation Physics Yao Wang, NYU 23

24 Photoelectric Effect An incoming photon interacts with the nucleus of an atom, causing ejection of a K-shell or L-shell electron (photoelectron) Atom completely absorbs incident photon and all energy is transferred The photoelectron propagates away with energy E e B The affected atom produces characteristic x-ray, while outer electrons fill the K-shell. Sometimes the characteristic x-ray transfers its energy to an outer electron (called Auger electron) Both photo electron and Auger electron are energetic electrons that can interact with the matter as discussed before E = hv Radiation Physics Yao Wang, NYU 24

25 Photoelectric Effect Radiation Physics Yao Wang, NYU 25

26 Compton Scattering An incoming photon ejects an outer shell electron, yielding a Compton electron The incident photon loses its energy and changes its direction (Not completely absorbed by the atom!) The scattered photon is called Compton photon Radiation Physics Yao Wang, NYU 26

27 The energy of the scattered photon depends on the scatter angle The maximum energy loss occurs when the photon is deflected backward (θ = 180 o ), backscattering When E is higher, more photons scatter forward The kinetic energy of the Compton electron = E-E Radiation Physics Yao Wang, NYU 27

28 Which interaction is better? Photoelectric effect helps to differentiate different human tissues/organs Compton scattering causes incident photons to deviate from straight path, and causes unnecessary exposure of x-ray to untargeted areas In medical imaging, we want to increase the likelihood of photoelectric events, while minimizing Compton scattering Radiation Physics Yao Wang, NYU 28

29 Probability of Photoelectric Effect Recall that a photoelectric event happens when incident photons interact with the Coulomb field of the nucleus of an atom More likely when colliding with an atom with more protons (i.e., larger Z number) Less likely when incident photons have higher energy (higher frequency) The probability increases abruptly when the photon energy rises above the binding energy of L-shell or K-shell electrons (so as to eject the electrons), then begins to diminish Rationale behind the use of contrast agent Z numbers: soft tissue: 7.4 soft, bone: 13.8 More contrast with low energy x-ray Photoelectric effect dominate over Compton scattering at low energy Radiation Physics Yao Wang, NYU 29

30 Probability of Compton Scattering Recall that Compton scattering occurs when an incident photon collides with outer shell electrons Likelihood proportional to the number of electrons per kilogram of the material (the electron density or ED) Relatively independent of incident photon energy in biological materials N AZ ED = W N Z W A : m : m Avogadro's number (atoms/mole) atomicnumber (electrons/atom) : molecular weight (grams/mole) ED is approximately constant for various biological material, ~ 3*10 26, except for hydrogen (6*10 26 ) Does not provide tissue contrast Radiation Physics Yao Wang, NYU 30

31 Relative Likelihood Compton scattering is equally likely in various materials and invariant of incident energy Photoelectric effect is more likely in high Z material and less likely with high incident energy Overall, Compton scattering is more dominant with higher incident energy in the same material But the percent of energy deposited due to photoelectric event is larger because all incident energy is absorbed. Radiation Physics Yao Wang, NYU 31

32 Measures of X-ray Beam: Photon Count N: number of photons A: area Radiation Physics Yao Wang, NYU 32

33 Measures of X-ray Beam: Energy Flow Radiation Physics Yao Wang, NYU 33

34 Spectrum of X-Ray The x-ray beam produced by an x-ray tube (mainly Bremsstrahlung) is polyenergetic (consisting photons with different energies or frequencies) X-ray spectrum S(E): The number of photons with energy E per unit area per unit time Radiation Physics Yao Wang, NYU 34

35 Spectrum of X-Ray Different curves are generated when different voltage potentials applied in a x-ray tube Generated when K-shell electrons are replaced by different outer shells When the incident electron collides with a nucleus Radiation Physics Yao Wang, NYU 35

36 Attenuation of X-ray Radiation: Homogeneous Slab N 0 Photons will be absorbed/deflected through the slab Let # of photons at x = N(x) # photons lost from position x to x+dx can be approximated by dn=n(x+dx)-n(x) = - μ N(x)dx, when dx is very small linear attenuation coefficient: μ μ is the fraction of photons that are lost per unit length The above can be rewritten as dn(x)/dx = - μ N(x). Integrate this from x=0 to x yields N(x) = N 0 exp{-μ x} The fundamental photon attenuation law Radiation Physics Yao Wang, NYU 36

37 Linear Attenuation Coefficients of Biological Tissues Radiation Physics Yao Wang, NYU 37

38 Homogeneous Slab Homogeneous slab: the attenuation rate is the same over the entire slab Radiation Physics Yao Wang, NYU 38

39 Half-Value Layer (HVL) Radiation Physics Yao Wang, NYU 39

40 Example Consider the image taken of a bar phantom uniformly irradiated by monoenergetic x-ray photons Assuming the bars are made of material that has a HVL of 0.2cm, and bars have thickness of 0.4 cm Assuming x-ray photons pass through the space between bars w/o attenuation Assuming the intensity of the image is proportional to the number of detected photons in a unit area What is the contrast of the resulting image? Go through in the class Radiation Physics Yao Wang, NYU 40

41 Radiation Physics Yao Wang, NYU 41

42 Non-Homogeneous Slab The attenuation coefficient depends on x Radiation Physics Yao Wang, NYU 42

43 Example: Two Layer Slab A slab with two homogeneous layers, with thickness d1, d2, and attenuation coefficients μ1, μ2. If the input X-ray intensity is N0, what is the intensity at the other end of the slab? Radiation Physics Yao Wang, NYU 43

44 Polyenergetic Photons The linear attenuation coefficient depends on the medium property as well as the energy of the incident photon (E) For a given material, μ can be denoted by μ(x;e) When the incident photons are polyenergetic, with spectrum S(E), the outgoing photon spectrum is In terms of intensity I = 0 I( x) { } x ( x'; E) dx S( x; E) = S ( E)exp µ E' S( E') de' = 0 S 0 0 ' 0 ( E') E'exp { } x µ ( x'; E') dx' 0 de' Radiation Physics Yao Wang, NYU 44

45 Radiation Dosimetry Previous topics deal with the production of radiation and measurement of radiation wave Radiation dosimetry considers the effect of radiation to the interacting media Exposure Dose Kerma Effective dose Radiation Physics Yao Wang, NYU 45

46 Exposure (Creation of Ions) Exposure (X) is measured in terms of the number of ions produced in a specific volume of air by EM radiation SI unit: C/kg Common unit: Roentgen (R) 1 C/kg = 3876 R Wilhelm Roentgen: Discovered X-ray, 1895, Nobel Prize 1901 Exposure decreases with distance from source (d) following a inverse square law X ( d) = X (0) / d 2 Radiation Physics Yao Wang, NYU 46

47 Dose (the deposition of energy) Radiation Physics Yao Wang, NYU 47

48 Kerma Radiation Physics Yao Wang, NYU 48

49 D = fx f - factor depends on material: f µ ρ = 0.87 µ ρ material air µ : mass attenuation coefficient ρ f = 0.87 for air f 1for soft - tissue Dose vs. Exposure See Table 4.6 for the mass attenuation coefficient of typical materials Radiation Physics Yao Wang, NYU 49

50 Equivalent and Effective Dose Dose equivalent The effect of radiation depends on the source of radiation (energy) Dose equivalent: H = D Q Q: quality factor Q = 1 for x-ray, gamma ray, electron, beta particle (used in medical imaging) Q = 10 for neutrons and protons Q = 20 for alpha particles Effective dose Effect of a dose also depends on the tissue type Effective dose measures the average effect over different tissue types D w effective j = organs :weighting factor for organ j D can be measured in rads, H can be measured in rems For a dose of 1 Gy and Q =1 -> H = 1 sievert (Sv) w j H Radiation Physics Yao Wang, NYU 50 j

51 Radiation Physics Yao Wang, NYU 51

52 Effective Dose of Different Tissues [Smith&Webb] Radiation Physics Yao Wang, NYU 52

53 Summary Ionization: ejection of an orbiting electron from an atom, the affected atom produces radiation in the process of returning to ground state Two types of ionizing radiation Particulate EM Particulate radiation transfers energy via Collisional transfer: resulting in heat Radioactive transfer: resulting in characteristic x-ray and Bremsstrahlung x-ray X-ray is produced by energetic electrons accelerated in a x-ray tube, consisting primarily Bremsstrahlung x-ray EM radiation transfers energy via Photoelectric effect: incident photons completely absorbed Compton scattering: incident photons are deflected X-ray imaging utilizes EM photoelectric effect caused by injected X-ray photons. Radiation Physics Yao Wang, NYU 53

54 Summary (cntd) Attenuation of EM radiation: Linear attenuation coefficient is the fraction of photons that are lost per unit length Depends on material property and the incident photon energy Fundamental photon attenuation law Homogeneous slab Heterogeneous slab Radiation dosimetry Exposure vs. dose: D=fX Equivalent dose: H=DQ Effective dose: D w effective j = organs w j H :weighting factor for organ j j Radiation Physics Yao Wang, NYU 54

55 Reference Prince and Links, Medical Imaging Signals and Systems, Chap 4. Radiation Physics Yao Wang, NYU 55

56 Reading: Homework Prince and Links, Medical Imaging Signals and Systems, Chap 4. Will be assigned at the end of lecture 3 and due on Friday Sept 29 Radiation Physics Yao Wang, NYU 56